'87 2.9L cooling issue - NOT HEADS

[Shocky]

I'm kind of going crazy. I replaced my radiator because the old one was literally disintegrating. I never had a leak and it wasn't having any overheating problems. Just simple old age. New rad went in like a charm, but now the heat doesn't work. I found out from here that I should "burp" the system and I have done so. twice on Saturday, three times on Sunday and once on Monday. It burps and I get a little heat from the vents, then it goes cold again. I also notice that when the system is cool, all the hoses collapse and the system is under a vacuum, identified by the sucking noise when I removed the cap form the radiator. I have replaced the cap with another new one.
As I said, it all worked fine until I replaced the radiator, so I don't think it's the heads.
I have a replacement heater-core, should I just change it out and get it over with?

 

[AndyB.]

Is the line from the radiator to the overflow tank clear? When under a vacuum, then center part of the inside of the cap should pull in and draw coolant from the overflow. It sounds like there is still air to be worked out.

 

[Shocky]

Is the line from the radiator to the overflow tank clear? When under a vacuum, then center part of the inside of the cap should pull in and draw coolant from the overflow. It sounds like there is still air to be worked out.

The overflow line is clear. That's why I got the new cap for it.